dy = lim [tex]\Delta[/tex]x-->0 (f(x+[tex]\Delta[/tex]x) - f(x)) dx = lim [tex]\Delta[/tex]x-->0 ([tex]\Delta[/tex]x) Therefore dy/dx is f'(x) if f(x) = y Is all of this true? I'm tired of integrating with variable substitution and not knowing what du by itself really means. People are always saying that Leibniz notation doesn't literally represent a fraction, and the seemingly algebraic manipulation is more complicated than it looks. But can't anyone say what exactly is going on? Maybe give me the rigorous definition of "dy" if I was wrong. Thanks. Oh, and if the above is correct, then can we say that dy/dx is a fraction of limits?